偶数维Riemannian流形的直径估计  

The Estimate of Diameter on Even Dimensional Riemannian Manifolds

作　　者：董莲莲[1] 王培合[1] 温玉亮[2] 

机构地区：[1]曲阜师范大学数学科学学院,山东曲阜273165 [2]华东师范大学数学系,上海200062

出　　处：《数学年刊（A辑）》2009年第6期787-792,共6页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No10871069);山东省自然科学青年基金(NoQ2008A08)资助的项目

摘　　要：设M^(2n)是2n维紧致无边单连通的Riemannian流形,S^(2n)为欧氏空间R^(2n+1)中的单位球面.探讨了满足截面曲率K_M∈(0,1],体积0<V(M)≤2(1+η)V(B_(3/4π))的流形M^(2n)的直径估计,这里η是某个仅依赖于n的正数,B_(3/4π)是S^(2n)上半径为3/4π的测地球,并且给出了这类流形上的一个gap现象及流形上Laplacian算子第一特征值的一个下界估计.Let M^2n be a 2n-dimensional compact, simply connected Riemannian manifold without boundary and S^2n be the unit sphere in Euclidean space R^2n＋1. The authors derive an estimate of the diameter in this note whenever the manifold concerned satisfies that the sectional curvature KM varies in （0,1] and the volume V（M） is not larger than 2（1＋η）V（B3/4π） for some positive number η depending only on n, where B3/4π is the geodesic ball on S^2n with radius 3/4π. A gap phenomenon of the manifold concerned is given and finally a lower bound of the first eigenvalue of Laplacian operator on manifold M is obtained.

关 键 词：直径 体积比较定理 Hausdorff收敛 

分 类 号：O186.12[理学—数学]